On corner scattering for operators of divergence form and applications to inverse scattering
On corner scattering for operators of divergence form and applications to inverse scattering
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DOI：
10.1080/03605302.2020.1843489
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发表时间：
2019-05
影响因子：
1.9
通讯作者：
F. Cakoni;Jingni Xiao
中科院分区：
文献类型：
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作者：
F. Cakoni;Jingni Xiao
摘要考虑了发散形式的“电导率”和低阶项的“势”均具有非均匀性的亥姆霍兹方程的散射问题。假定非均匀性的支撑包含一个凸角。我们证明，在适当假设拐角附近的电势和电导率的情况下，由于拐角的存在，任何入射场都会发生散射。在角散射分析的基础上，给出了从单入射波对应的散射数据确定可容许非均匀性支撑的多边形凸壳的唯一性结果。这些结果只要求系数在拐角附近有一定的规律性来模拟非均匀性，而在拐角之外，它们可以是相当普遍的。我们的散射和逆散射的主要结果是建立的，而一些分析工具是在任何维度上发展起来的
Abstract We consider the scattering problem governed by the Helmholtz equation with inhomogeneity in both “conductivity” in the divergence form and “potential” in the lower order term. The support of the inhomogeneity is assumed to contain a convex corner. We prove that, due to the presence of such corner under appropriate assumptions on the potential and conductivity in the vicinity of the corner, any incident field scatters. Based on corner scattering analysis we present a uniqueness result on determination of the polygonal convex hull of the support of admissible inhomogeneities, from scattering data corresponding to one single incident wave. These results require only certain regularity around the corner for the coefficients modeling the inhomogeneity, whereas away from the corner they can be quite general. Our main results on scattering and inverse scattering are established for while some analytic tools are developed in any dimension